Balancing Multiplayer Games – Opportunity, Power and Relativity

Overview

This article covers three balance design concepts. The application of these concepts is geared towards improving a game’s decision quality and variety.

Balance and Fun

Balance is an important part of the design effort as it ensures a number of compelling options are always made available to the player. Ideally, the player is always put in a position where they must weigh the consequences of their actions. In turn, this contributes to a game’s challenge. In the absence of challenge, a game is likely to feel rudimentary or redundant as it lacks an opportunity for skill development and mastery. Skill development and mastery heavily influence a game’s fun factor. Therefore, the absence of balance will compromise the player’s capacity to experience ‘fun’ within a game.

Note: This section was added to highlight my assumptions as a designer. These assumptions are based on my experiences and findings. I am always interested in hearing new perspectives, I hope this article causes you to reflect on your own assumptions; if so, please do share. There is a great quote I read the other day which I feel echos this quite well, “when you talk (or write), you only repeat what you already know. But if you listen, you may learn something new.” (J.P. McEvoy)

Game Balance Design Considerations

The three concepts we will explore today are opportunity cost, power concentration, and relative balance. My focus will be on explaining the logic and theory behind each concept. Please note that the concepts below have multiple applications which can vary depending on the considerations of each game.

Opportunity Cost

Each time the player makes a choice, they do so at a cost. Although this concept is called opportunity cost, its not exactly the same as its microeconomics counterpart. The cost of opportunity can come in many forms. It can be in the form of time, advantage, or even strategic positioning. For example, in a real time strategy game players often have to decide between immediate benefits and delayed benefits; do I purchase this cheap 100 resource unit or do I save up for this expensive and powerful 1000 resource unit. In this example, the primary cost is time in the form of idled resources (saving up for the expensive unit) and the secondary cost is strategic positioning. As the player waits to accumulate resources, they temporarily give up the opportunity to field units therefore relinquishing map control. The benefit is presumably long-term advantage, the expensive unit should perform better than its counterparts.

Applying this concept simply requires us to account for the opportunity cost of each decision in a game. If a decision has a very low opportunity cost, then I typically ignore it. When this is not the case, I create designer rules to account for it. For example, in Company of Heroes 2, the more expensive a unit the better the return on investment. When comparing relative cost, we made heavy tanks approximately 30-40% more powerful than their counterparts. Prior to this adjustment, heavy tanks were extremely difficult to field because the cost was just too high. This was a very direct and readable modification to this unit type, which in turn made heavy tanks viable.

Power Concentration and Relative Balance

Power concentration can either be a positive or a negative characteristic depending on the framework of a game. It typically means the value of an object grows exponentially the more power that is assigned to it. Relative balance considers the interactions of each unit versus all others. For example, on Company of Heroes 2, we determined that power concentration was a favourable characteristic but at times was undermined by relative balance. Consider the example below:

Player 1

Sherman Tank: 3 Damage | 7 Health
Sherman Tank: 3 Damage | 7 Health

VS.

Player 2

Tiger Tank: 8 Damage | 10 Health

If you refer back to my previous article for reference on the calculations, Balancing Multiplayer Games – Intuition, Iteration and Numbers, you will find that Player 1 has a total army value of √(3*7)*2 = 9.16 and Player 2 has a total army value of √(8*10) = 8.94. Given these conditions, who is more likely to win the engagement assuming each tank is allowed to fire once per round? It is more likely that Player 2, even with a lower total army value of 8.94 vs. 9.16, will win this engagement. This is largely the result of power concentration and the relative balance of these units to one another. After the first round, Player 2’s Tiger is reduced to 4 health; whereas, Player 1 has lost an entire tank. This effectively cuts the total army value of Player 1 by half. The following round sees the second Sherman knocked out and the Tiger reduced to 1 health. This demonstrates one of the potential values of concentrating power; the Tiger is better able to maintain its throughput over the course of the rounds. Now this battle could have easily gone the other way, depending on how damage and health is allocated. To highlight the effect of relative balance, consider this next example:

Player 1

Sherman Tank: 5 Damage | 5 Health
Sherman Tank: 5 Damage | 5 Health

VS.

Player 2

Tiger Tank: 10 Damage | 10 Health

In this example, Player 1 has a total army value of √(5*5)*2 = 10 and Player 2 has a total army value of √(10*10) = 10. Given these conditions, who is more likely to win the engagement assuming each tank is allowed to fire once per round? The answer is Player 1 despite the power concentration of the Tiger. After the first round, Player 1 would have lost one Sherman Tank; whereas, Player 2 would have lost his Tiger tank. The combined damage of the two Sherman tanks is 10, which is enough damage to destroy the Tiger tank at the end of the first round. This leaves Player 1 with one Sherman tank and Player 2 with no tanks. This demonstrates the impact of relative balance. Even though the army values were kept relatively the same, the distribution of combat characteristics greatly affected the engagements outcome. The main reason the Tiger lost in the second example was because it did far too much damage than what was needed. To further demonstrate this concept, consider this modification to Player 2:

Player 1

Sherman Tank: 5 Damage | 5 Health
Sherman Tank: 5 Damage | 5 Health

VS.

Player 2

Tiger Tank: 5 Damage | 20 Health

The Tiger has the exact same total army value as before, √(5*20) = 10. With that in mind, who is more likely to win this engagement? The answer is Player 2 largely because there is no damage inefficiency on the Tiger relative to the Sherman. By the end of the second round, the Tiger tank would have 5 health remaining and would have knocked out both Sherman tanks. Relative balance seeks to modifity the relationships or interactions within a game to better control the outcomes. To establish good relative balance in a game, I generally establish designer rules when creating any content. Going back to our example above, if the Sherman is a medium tank and the Tiger is a heavy tank, I might define upper and lower limits on health and damage for each unit type. Meaning, all medium tanks would have health and damage between a range of X and Y. By establishing this type of framework, I can better define the expected outcomes and take the necessary actions to account for them. If I just randomly assigned values to units without considering how those values affect interactions within the game, it is likely that unintentional consequences would result. Things become more challenging as you begin to factor in more considerations, for that reason I tend to take a more methodological approach to better organize myself.

Note: The value of the more expensive unit does not have to be restricted to the distribution of its combat characteristics. In this example, there is also a cost associated with microing multiple units over just one. Controlling 10 Shermans is likely far more difficult than controlling 3 Tigers; this is a concept we will explore in a future article. What I hope these examples highlight is the complex matrix of decisions we as designers must account for in order to ensure that the outcomes of our game match our intents. By carefully crafting the decision matrix, we ensure that players continually have compelling options to choose from.

Conclusion

The design considerations amongst opportunity cost, power concentration, and relative balance all play off of one another. These concepts are based on the same processes players will employ when trying to determine their best course of action. They may not do so consciously, but they will come to very similar conclusions nonetheless. By accounting for the player’s considerations, we can then better craft the decision matrix thereby improving a game’s decision quality and variety.

Power concentration and relative balance are factors that exist, but are not accounted for by your scoring function. One hint that your scoring function is not optimized for the simulation is that the unit of measure of your scoring function is nonsensical.

The Sherman’s Damage is not “5”, it is “5 per round”
The Sherman’s Health is “5”, not “5 per round”

The square root of (const per round * const) leads to an arbitrary unit which doesn’t make much sense. Try breaking down your scoring function into an instance score (ie, value of a unit in the current turn) vs a simulation score (value of a unit over the course of x number of turns, or over a simulation). Once the two functions are defined, the delta in their score will reveal the value of their “power concentration” and “relative balance” (bundled into a single score, but that too can be broken down with further scoring functions).

I see your point but keep in mind the total army value was just meant to be a quick and rough way to compare each player’s units at the start of a round, nothing more. Your points on creating an instance score and simulation score are spot on though.

Hey, really nice series detailing how multiplayer games work.
I have written a few articles about multiplayer games too. A little more oriented to the System Architecture side of things. I’m happy to see that more people are interested and putting effort on making multiplayer games better.
Feel free to check my site http://www.game-savvy.com. I would greatly appreciate some feedback too.